Structural Change and Global Trade

K.7 Structural Change and Global Trade Lewis, Logan T., Ryan Monarch, Michael Sposi, and Jing Zhang Please cite paper as: Lewis, Logan T., Ryan Monarch, Michael Sposi, and Jing Zhang. (2018). Structural Change and Global Trade. International Finance Discussion Papers 1225. https://doi.org/10.17016/IFDP.2018.1225 International Finance Discussion Papers Board of Governors of the Federal Reserve System Number 1225 April 2018

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1225 April 2018 Structural Change and Global Trade Logan T. Lewis, Ryan Monarch, Michael Sposi, and Jing Zhang NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Structural Change and Global Trade LoganT.Lewis RyanMonarch FederalReserveBoard FederalReserveBoard MichaelSposi JingZhang FederalReserveBankofDallas FederalReserveBankofChicago April 2018 Abstract Services, which are less traded than goods, rose from 50 percent of world expenditure in 1970to80percentin2015. Suchstructuralchangerestrained“openness”—theratioofworld tradetoworldGDP—overthisperiod. Wequantifythiswithageneralequilibriumtrademodel featuring non-homothetic preferences and input-output linkages. Openness would have been 70 percent in 2015, 23 percentage points higher than the data, if expenditure patterns were unchangedfrom1970.Structuralchangeiscriticalforestimatingthedynamicsoftradebarriers and welfare gains from trade. Ongoing structural change implies declining openness, even absentrisingprotectionism. JELclassifications: F41,L16,O41 Keywords: Globalization,StructuralChange,InternationalTrade TheviewsexpressedhereshouldnotbeinterpretedasreflectingtheviewsoftheFederalReserveBoardofGovernors,the FederalReserveBankofChicago,theFederalReserveBankofDallas,oranyotherpersonassociatedwiththeFederal ReserveSystem. WethankKeremCos¸ar,ColinHottman,KiminoriMatsuyama,MartiMestieri,TomaszS´wie˛cki,and Kei-MuYiforusefulcomments.ThispaperalsobenefitedfromaudiencesattheChicagoFed,theFederalReserveBoard, theInternationalMonetaryFund,theUniversityofCaliforniaatSantaCruz,theUniversityofPittsburgh,theUniversity ofWesternOntario,andtheUniversityofWisconsinaswellasparticipantsatthe2017SocietyforEconomicDynamics Conference,2017BNM/IMFConferenceonChallengestoGlobalization,2017EIITconference,Spring2017Midwest Macroeconomics Meetings, Spring 2017 Midwest International Trade Meetings, and 2018 AEA Meetings. Victoria Perez-Zetuneprovidedexcellentresearchassistance.

1 Introduction TheratioofworldtradetoworldGDPincreasedfrom19percentto48percentfrom1970to2015. Thisremarkablegrowthin“openness"occurredoverthesameperiodthattheworld(andindividual countries) experienced a seismic shift in the composition of total spending; global spending on servicesrosefromabouthalfofworldexpendituresin1970to80percentin2015. Thisphenomenon of “structural change" is thoroughly studied and is well known to be a foundational component of economic growth and development. Less appreciated, however, are the implications of structural changeonglobaltrade,giventhatservicesaremuchlesstradedinternationallythangoods. Indeed, yearswhenservicesgrewfastertendedtobeexactlythoseinwhichopennessgrewmoreslowly. Since an ever-greater share of the world economy has been devoted to services—less-tradable consumption categories—it must be that structural change held back trade flows during this time, and could potentially lead to declines going forward. Using a multi-country, multi-sector trade modelwithnon-homotheticpreferencesandinput-outputlinkages, thispaperquantifiestheeffects of structural change on global trade flows over the years 1970–2015. Moreover, we identify the channels through which those effects are realized and demonstrate the importance of the ongoing processofstructuralchangeinthemeasurementoftradebarriersandthegainsfromtrade. Westartwithareduced-formcounterfactualcomputationofopennesswithoutstructuralchange; weassumethattheshareofexpenditureoneachsectorisfixedattheinitialyearofdata,whileeach sectoral trade-to-expenditure ratio (i.e., “sectoral openness”) rises exactly as in the data. We find that openness in 2015 would have been 91 percent, or 43 percentage points higher than in the data. This simple calculation suggests that shifting toward less-tradable consumption substantially suppressedtradegrowthinthelastfivedecades. Atthesametime,assumingthatsectoralopenness in the absence of structural change evolved exactly as it did in the real world is unpalatable; the underlyingforcesdrivingstructuralchange, suchasgrowthinsectoralproductivityandreductions in trade costs, must also have affected sectoral openness. The linked interactions between these factorsthereforecallforageneralequilibriummodeltocapturethefulleffectofstructuralchange ontrade. Forthisreason, webuildamulticountry, multisector, Ricardiantrademodelthatincorporates endogenousstructuralchangeandtradepatternsovertime,similartoUy,YiandZhang(2013)and Sposi (2016). On the production side, a continuum of varieties in each sector are produced with labor and intermediates. Countries differ in their sectoral productivity and trade barriers, forming thebasisforcomparativeadvantage. Thedynamicbehaviorofproductivityandbilateraltradecosts at the sector level influences the patterns of production and trade over time. On the demand side, we adopt non-homothetic preferences that allow total income and relative prices to shape sectoral expenditureshares,asinComin,LashkariandMestieri(2015). We calibrate the underlying structural parameters and time-varying processes of the model to 1

relevant observables in 26 countries and a rest-of-world aggregate from 1970-2015. Using data on sectoralexpenditureshares,sectoralprices,andemploymentlevels,weestimatethekeypreference parameters,namelytheelasticityofsubstitutionbetweengoodsandservicesandtheincomeelasticityofdemandforgoodsandservices. Couplingthesewithinput-outputcoefficientsfromtheWorld Input-OutputDatabaseandbilateraltradedataenablesustobackoutestimatesofproductivityand tradecostsfromthestructuralequationsofthemodel. After solving the model, we conduct a counterfactual similar to the reduced-form one. We deliver constant expenditure shares for all sectors in each country across time by setting both the elasticity of substitution and the income elasticity to 1. The model differs from the reduced-form calculationinthatitallowsforanimpactofthecounterfactualexpendituresharesonthepricesfor goodsandservicesandonendogenousfactorprices,allofwhichwillaffectsectoralopenness. We show that the model-based counterfactual still implies a substantial increase in the global trade-toexpenditureratio,reaching70percentby2015asopposedto48percentinthedata. Themagnitude that structural change has restrained trade flows is on par with the magnitude that declining trade costsboostedtradeflowsoverthesametimeperiod. Importantly, the model-based effect of structural change on world openness (23 percentage points) is smaller than the reduced-form one (43 percentage points). Why is this the case? The primary reason is that “goods openness”—the ratio of goods trade over goods expenditure—in the counterfactualissubstantiallylowerthaninthedata. Whenfixingtheexpendituresharesatthe1970 level,thegoodsexpendituresharerisesrelativetothebaseline;however,asaresultofinput-output linkagesweakeningtheoveralleffect,goodstradedoesnotrisebythesamedegree. Omitting structural change has implications for the measurement of two of the most important unobservables in international trade theory: trade costs and the gains from trade. Trade costs inferred from a one-sector model using aggregate trade flows barely decline during periods when structuralchangewasprominent. Specifically,whentradegrowthdiminishedasaresultofincreased services expenditures, as in the years 1980–2000, such a model would attribute this trend to rising protectionism or slower declines in trade costs. In contrast, using the same underlying trade flow data, our model with structural change delivers larger declines in trade costs, which is consistent withtheincreasedtradeintegrationmeasuresduringthisperiod. Ourestimatesofthegainsfromtradearelowerthanthanthoseestimatedusingotherwisesimilarmodelsthatignorestructuralchange. Thelogicunderpinningthisfindingstemsfromthefeature that changes in trade costs endogenously affect sectoral expenditure shares. In the typical multisectorframework,thewelfaregainsfromtrade—thepercentchangeinconsumptionwhenmoving fromautarkytoopentrade—areaweightedaverageofconsumptiongainscomingfromeachsector, wheretheweightsaredeterminedbysectoralexpenditureshares. And,sincegoodsaretradedmore intensively than services, consumption generally increases by more in goods than in services. In our model of structural change, however, opening up to trade will change those sectoral expendi- 2

tureshares, throughthefollowingtwochannels: (i)adeclineintherelativepriceofgoodsand(ii) an increase in aggregate income. Both of these features imply a decline in the goods expenditure share, dampening the gains accrued through higher levels of goods consumption. In other words, the aggregate gains are suppressed by the endogenous response of expenditure shares, a clear differencebetweenourworkandpriorliterature,suchasCostinotandRodríguez-Clare(2014),where expendituresharesaretreatedasexogenous. Animportantcorollaryisthatasstructuralchangepersists over time, the measured gains from trade will be increasingly suppressed. Finally, emerging economies,whichtendtohavehighergoodsexpenditureshares,alsotendtohavehighergainsfrom tradecomparedtoadvancedeconomies. Projecting our model into the future indicates that openness has essentially peaked, and will decline to around 40 percent by 2030. Importantly, this occurs without any changes in trade costs, meaning that the downward trend in trade relative to GDP is driven by the effects of increased services consumption. At the same time, there is little evidence that the slowdown in international tradegrowththatstartedin2011isaresultofstructuralchange; thatis,structuralchangehasbeen adragontradegrowthfordecades,andthedraghasnotbeenstrongerinrecentyears. A well-established literature documents how international trade and openness affect structural change. Matsuyama (2009) emphasizes that trade can alter patterns of structural change and that using closed-economy models may be insufficient. Uy et al. (2013) find that rapid productivity growth in South Korea’s manufacturing sector contributed to a rise in manufacturing employment shareduetoimprovedcomparativeadvantage. Inaclosedeconomy, thesameproductivitygrowth would have produced a decline in the manufacturing share. Betts, Giri and Verma (2017) explore theeffectsofSouthKorea’stradepoliciesonstructuralchange,findingthatthesepoliciesraisedthe industrial employment share and hastened industrialization in general. Teignier (2016) finds that internationaltradeinagriculturalgoodsaffectedstructuralchangeintheUnitedKingdomevenmore thanSouthKorea. Weshowinthispaperthatstructuralchangemayinfactbemoreconsequential for international trade than international trade is for explaining the pattern of structural change in manycountries. More broadly, our findings point to structural change as being an important link between international trade and economic development. McMillan and Rodrik (2011) find that the effect of structuralchangeongrowthdependsonacountry’sexportpattern,specificallythedegreetowhich a country exports natural resources. Cravino and Sotelo (2017) show that structural change originating from greater manufacturing trade increases the skill premium, particularly in developing countries. Sposi (2016) documents how the input-output structures of advanced economies are systematically different from those of developing economies, which contributes to systematic differences in resource allocations between rich and poor countries. Markusen (2013) shows how, among other things, including non-homothetic preferences into a Hecksher-Ohlin model can help explainwhyweobservelesstradethanpredictedbymodelswithoutnon-homotheticities. 3

Someanalysissuggeststhatinternationaltradeplaysonlyasmallroleinexplainingthepattern of structural change. Kehoe, Ruhl and Steinberg (2017) find that for the United States, relatively faster growth in manufacturing productivity was the primary cause for reduced employment in the goods-producingsector,withasmallerrolefortradedeficits. S´wie˛cki(2017)alsofindsdifferential productivitygrowthismoreimportantonaverageinexplainingstructuralchangethanothermechanisms, including international trade. Nonetheless, even if international trade only contributes a small portion to structural change, we show that structural change plays a large role in the growth ofworldtrade. Non-homotheticpreferencesareimportantinunderstandingotheraspectsofinternationaltrade as well. Fieler (2011) finds that non-homothetic preferences can explain why trade grows with income per capita but not population. Simonovska (2015) shows that non-homothetic preferences canmatchthepatternfoundinthedatathathigher-incomecountrieshavehigherpricesoftradable goods. Matsuyama(2015)andMatsuyama(2017)showthatnon-homotheticpreferencescombined withhomemarketeffectscanleadtohigh-incomecountriesproducingandexportinghigherincome elasticitygoodswithoutassumingtheyhaveanexogenouscomparativeadvantageinsuchgoods. Finally, thispaperalsocontributestoanearlierliteratureonhowglobaltradegrowsrelativeto GDP. In an early theoretical contribution, Markusen (1986) includes non-homothetic preferences in a trade model to be consistent with empirical evidence of a relationship between income and trade volumes. Rose (1991) shows that increases in income and international reserves along with decliningtariffrateshelpexplainthedifferencesintradegrowthacrosscountriesoverthreedecades. Krugman,CooperandSrinivasan(1995)analyzesthegrowthinworldtradesinceWorldWarIIand potential consequences for labor markets. Baier and Bergstrand (2001) find that income growth explainsnearlytwo-thirdsoftheincreaseinglobaltrade,withtariffsexplaininganadditionalonequarter. Imbs and Wacziarg (2003) document a U-shaped pattern of specialization as countries becomericher;theyfirstdiversifyacrossindustriesandonlylaterspecializeastheygrow. Yi(2003) shows how vertical specialization, the splitting of production stages across borders, can amplify grosstraderelativetovalue-addedtradeandhelpexplainthelargeincreasesintrade-to-GDPratios. Theremainderofthepaperproceedsasfollows. Section2describesthereduced-formcounterfactual,whileSection3setsupthegeneralequilibriummodelwithendogenoustradeandconsumptionshares. Section4describesthecalibrationandsolutionofthemodel,whileSection5presents thequantitativeresults. Section6concludes. 2 Empirics and a Reduced-Form Counterfactual TheratioofglobaltradetoGDProsefromabout20percentto50percentbetween1970and2010 before flattening through 2015. How would this trend have differed without the significant shift in expenditures from goods to services over that time? This section presents a direct and simplified 4

answer to the question by holding each country’s expenditure share on goods and services fixed at its1970levelandtracingoutacounterfactualpathfortheglobaltrade-to-GDPratio. Thisapproach willprovideapreliminaryideaofhowstructuralchangeaffectedglobaltradegrowth. 2.1 Data We begin by laying out the key concepts for our exercise and describing how we capture them in thedata. First,somedefinitions: Expenditurereferstofinaldemand: consumption,investmentand governmentspending. Structuralchangereferstochangesintheexpenditureofgoodsandservices as a share of total expenditure over time. And openness is defined as total trade (imports plus exports)asashareofexpenditure, withsectoralopennessdefinedanalogouslyatthesector(either goodsorservices)level. Foreverycountry(andfortheworldasawhole),wecandecomposeopennessinperiodt as Trade Trade Exp Trade Exp t gt gt st st = + , (1) Exp Exp Exp Exp Exp t gt t st t wheregandsdenotegoodsandservices. Clearly,changesinsectoralopenness Tradekt,andsectoral Expkt expenditureshares Expkt,shapetheopennessmeasureovertime. Expt Wegatherdataneededtodothebreakdowninequation(1)for26countriesandarest-of-world aggregate over the period 1970–2015.1 In UN nomenclature, we take the goods sector to consist of “agriculture, hunting, forestry, fishing” and “mining, manufacturing, utilities,” while services include “construction,” “wholesale, retail trade, restaurants, and hotels,” “transport, storage, and communication,” and “other activities”. The World Input-Output Database (WIOD) contains data onsectoraltradeandexpenditurefortheyears1995–2011—webuildaroundthissubsetofyearsto generatedataforallotheryearsinoursample. Extendingthetradedataisstraightforward. AsdetailedinAppendixA,wetakelonger-running country-level sectoral trade data from various data sources, and then generate a splicing factor betweenitandWIODdatainoverlappingyears. Usingthissplicingfactoronthelonger-runningdata, wecanthenextendtheseriesbackto1970–1994andforwardto2012–2015. Theprocedureforgeneratingsectoralexpendituredataismoreinvolved,asthereisnowidelyavailable companion data available for our sample to splice with the WIOD. As a workaround, we take a long time series of data on sectoral value added (available from the United Nations Main AggregatesDatabase)andconvertitintosectoralgrossoutputusingaveragevalue-added-to-grossoutput ratios from the WIOD. Then, subtracting sectoral net exports (coming from our trade data described above) from sectoral gross output generates sectoral absorption, which is equal to final demandforasector(i.e. sectoralexpenditure)plusallusageofthatsectorasanintermediateinput. 1ThefulllistofcountriesislistedinAppendixA. 5

Inotherwords, domesticusageofthatsectorisabsorbedeitherbyconsumersorbyfirms. Finally, using average input-output coefficients from the WIOD, we can calculate what fraction of sectoral absorptionwenttointermediateusage.2 Theremainingamountcorrespondstosectoralexpenditure. Astylizeddepictionofthiscalculationisinfigure1.3 Figure1: Derivingsectoralexpendituresfromsectoralvalueadded Production Consumption Net Value Added Expenditure (Multiply by (Subtract input GO/VA ratio) usage) (Add imports, subtract exports) Gross Gross Output Absorption Note:Categoriesinbluerepresentpubliclyavailabledata,whilecategoriesinblackrepresentimputedmoments. 2.2 OpennessandStructuralChange This section describes the patterns of openness and structural change in the world economy found inequation(1). Figure2,panel(a)showsthetrendinopenness,whichwas19percentin1970and reached55percentby2008. Opennessgrewstronglyformuchoftheperiod,acceleratinginthelate 1990sand2000s. Since2011,theratiohasbeennearlyflatatabout50percent. Even while this trend was taking place, world consumption shifted to services. Figure 2 panel (b) demonstrates the substantial shift in expenditures from goods to services from 1970 to 2015. The service share increased steadily over the period by a total of 27 percentage points, from 53 percentin1970to80percentin2015. Ifthesetwosectorswerebothtradedinternationallywithsimilarintensities,theimpactofstructural change on openness would be small. In the data, however, openness significantly differs between the two sectors. Figure 2 Panel (c) plots the ratio of sectoral trade to sectoral expenditure over1970-2015. Clearly,goodsaremuchmoreopenthanservices;theratiooftradetoexpenditure was about 6 percent for services but was 33 percent for goods in 1970. Over time, trade openness 2MoredetailonthisstepcanbefoundinSposi(2016). 3NotethatthisprocedureexactlyreplicatesthesectoralexpendituredataintheWIODfor1995through2011. 6

Figure2: Opennessandstructuralchange 0.6 1 2 Goods Goods Services Services 0.5 0.8 1.5 0.4 0.6 1 0.3 0.4 0.5 0.2 0.2 0.1 0 0 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Year Year Year (a)Openness (b)SectoralExpenditureShares (c)SectoralOpenness increasedforbothsectorsbutwasmuchmorepronouncedforgoods. Bytheendoftheperiod,the trade-expenditureratiowasabout14percentforservicesand180percentforgoods.4 Considering these three figures together presents a puzzle of sorts: How could trade grow so quickly while a relatively less-traded sector gained expenditure share? The answer is that trade grew spectacularly in spite of the ongoing transition to services in the world economy, meaning structural change held back even greater increases in trade. This dynamic becomes apparent when calculatingthecorrelationbetweenthegrowthratesofopennessandtheservicesexpenditureshare. For the world, the correlation is −0.72, meaning that periods of faster openness growth feature a slower-growing service share. The same result holds when calculating 10-year rolling correlations betweenthegrowthratesofthetwoseries,asshowninfigure3. The finding that a faster shift to services reduces growth in openness is also present at the countrylevel. Table1showstheresultsofregressingthecountry-levelgrowthrateofopennesson thecountry-levelgrowthrateoftheserviceshareforthe27countries(including“RestofWorld”)in oursample. Again,wefindstrongevidenceofanegativecorrelation;whenacountryfeaturedhigher growth in its service expenditure share, it experienced lower growth in openness, even accounting foritslevelofpercapitaincome. Inthenextsubsection,wepresentasimplifiedviewofhowmuch structuralchangeheldbackglobaltradegrowth. 4The ratio of trade to expenditure can be over 100 percent for two reasons. First, trade here refers to the sum of importandexports.Second,tradeisagrossmeasure(asaresultoftradeininputs)andexpenditureisafinalconsumption measure. 7

Figure3: 10-Yearrollingcorrelations,growthrateofopennessandserviceshare -0.6 -0.65 -0.7 -0.75 -0.8 -0.85 -0.9 -0.95 1980 1985 1990 1995 2000 2005 2010 2015 Year Table1: Country-levelopennessandserviceshare DependentVariable: OpennessGrowth ServicesShareGrowth -0.464∗∗∗ -0.459∗∗∗ -0.220∗∗∗ -0.235∗∗∗ (0.157) (0.156) (0.062) (0.061) LogPer-CapitaGDP -0.039∗∗∗ -0.070∗∗∗ (0.011) (0.010) YearFE NO NO YES YES CountryFE YES YES YES YES N 1215 1215 1215 1215 R2 0.07 0.08 0.33 0.36 Note: Robuststandarderrorsareinparentheses,with∗∗∗ significanceatthe99percentlevel,∗∗ atthe95percentlevel, and∗atthe90percentlevel. 2.3 AReduced-FormCounterfactual To gauge the contribution of structural change to openness, we return to equation (1), but freeze theexpendituresharesatthefirstperiodofdata. Wecannowcomputeacounterfactualmeasureof opennessas: (cid:94) Trade Trade Exp Trade Exp t = gt g0 + st s0 . (2) Exp Exp Exp Exp Exp t gt 0 st 0 Byholdingtheexpendituresharesofsectorkfixedatthefirstperiod,weshutdowntheprocess (cid:94) of structural change in the data. The counterfactual openness measure, Tradet, is free of structural Expt 8

change, but it is consistent with the observed sectoral openness. We calculate counterfactual trade opennessforeachcountryandtheworldeconomy. Ifopennessinthecounterfactualissignificantly differentfromthedata,itsuggeststhatstructuralchangehasanimportantimpactonopenness. Figure 4 contrasts the aggregate trade openness measure in the data with the reduced-form counterfactual. The gap between the counterfactual openness measure and the actual data widens substantiallyoverthe1990sandearly2000s,indicatingthatwithoutunderlyingmovementstoward less-tradableservices,globaltradegrowthwouldhavebeenfargreater. Accordingtothisexercise, as of 2015, persistent structural change since 1970 has lopped about 45 percentage points off the ratiooftradetoexpenditure. Figure4: Openness 1 Data Fixed expenditure weights 0.8 0.6 0.4 0.2 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 Year Note:Thedatalineistheaggregatetradetoexpenditureratiofor26countrieslistedinthedataappendix,plusarest-ofworldaggregate.Thecounterfactuallineholdstheexpendituresharesconstantatthestartofthesample. Of course, this reduced-form exercise has a major deficiency: Sectoral trade openness was jointlyaffectedbythesameforcesthatinstigatedstructuralchange. Thedynamicsofsectoralproductivity and trade barriers not only affect expenditure shares through relative prices and income levels but also affect sectoral openness through comparative advantage and trade flows. Additionally, input-output linkages are also critical for identifying how changing expenditure shares feed through into production and trade. Thus, a structural model incorporating these endogenous relationships and featuring intermediate input-output linkages is needed to quantify the impact of structuralchangeoninternationaltrade. 9

3 Model We consider a multi-country, two-sector Eaton Kortum trade model of the global economy with non-homothetic preferences. There are I countries and the two sectors are goods (g) and services (s). Householdpreferenceshavenon-unitaryincomeandsubstitutionelasticitiesofdemand. Ineach sector, there is a continuum of goods, and production uses both labor and intermediate inputs. All goodsaretradable, buttradecostsvaryacrosssectors, country-pairs, andovertime. Productivities also differ in initial levels and subsequent growth rates across sectors and countries. These timevarying forces drive structural change. Unless needed for clarification, we omit the time subscript below. 3.1 EndowmentsandPreferences Labor is perfectly mobile across sectors within a country, but immobile across countries. Let L i denote total labor endowment in country i, which varies over time, and L denote labor employed ik insectork. Thefactormarketclearingconditionisgivenby: L =L +L . (3) i ig is ThehouseholdincountryihasastandardperiodutilityfunctionU(C)overthelevelofaggrei gateconsumption,C. Aggregateconsumptioncombinessectoralcompositegoodsaccordingtothe i implicitlydefinedfunction: (cid:18) (cid:19)εk−σ (cid:18) (cid:19)σ−1 ∑ ω C i σ C ik σ =1, (4) k L L k=g,s i i whereforeachsectork∈{g,s},C isconsumptionofthesector-kcompositegood,andthepreferik enceshareparameters,ω ,arepositiveandsumtooneacrosssectors. Theelasticityofsubstitution k across sectoral composite goods is σ >0. If σ >1, the sectoral composite goods are substitutes, and if σ ≤1, the sectoral composite goods are complements. ε denotes the income elasticity of k demandforsectork. This set of preferences (known as “normalized Constant Elasticity of Substitution”) was first studiedbyGorman(1965)andHanoch(1975)andwasfoundtobeespeciallyaptforstudyinglongrun structural change by Comin et al. (2015). Comin et al. (2015) show that this specification of nonhomotheticpreferenceshastwoattractiveproperties. First,theelasticityoftherelativedemand forthetwosectoralcompositeswithrespecttoconsumptionisconstant. ThiscontrastswithStone- Geary preferences, where the elasticity of relative demand goes to zero as income or aggregate consumptionrises—apredictionatoddswiththedatabothatthemacroandmicrolevels. Second, the elasticity of substitution between sectoral composites, given by σ, is constant over income, 10

meaningthatthereisnofunctionalrelationshipbetweenincomeandsubstitutionelasticities.5 They demonstrate that this specification has the potential to be flexible enough to capture the structural changepatternsinthedata. Therepresentativehouseholdmaximizesaggregateconsumptionineachperiod,C,bychoosing i sectoralconsumptionlevels,C ,subjecttothefollowingbudgetconstraint: ik P C +P C +ρwL =wL +RL, (5) ig ig is is i i i i i i (cid:124) (cid:123)(cid:122) (cid:125) PiCi wherew andP denotethewagerateandthepriceofthesector-kcompositegood,respectively,and i ik P denotes the “ideal” aggregate consumption price. The household supplies its labor endowment i inelastically and spends its labor income on consumption. A fraction ρ of income is sent into a i globalportfolio,andtheportfoliodispersesRinlumpsumequallyacrosscountriesonaper-worker basis. ρ variesovertimeandRisdeterminedbyglobalportfoliobalanceineachperiod. Therefore, i each country lends, on net, ρwL −RL to the rest of the world. This aspect enables the model to i i i i tractably match aggregate trade imbalances in the data, as in Caliendo, Parro, Rossi-Hansberg and Sarte(2016). Thefirst-orderconditionsimplythattheconsumptiondemandofsectoralgoodssatisfies: (cid:18) P (cid:19)−σ(cid:18) C (cid:19)εk C =Lωσ ik i , (6) ik i k P L i i wheretheidealaggregatepriceisgivenby: (cid:34) (cid:35) 1 L (cid:18) C (cid:19)εk−σ 1−σ P = i ∑ ωσ i P1−σ . (7) i C k L ik i k=g,s i Thesectoralexpendituresharesaregivenby: P C (cid:18) P (cid:19)1−σ(cid:18) C (cid:19)εk−1 e = ik ik =ωσ ik i . (8) ik PC k P L i i i i Thus, how relative price and real income per capita shape the sectoral expenditure shares are governed by the elasticity of substitution between sectors σ and the sectoral elasticity of income ε . k Specifically, when σ < 1, a rising sectoral relative price pushes up the expenditure share in that sector,andviceversa. Whenasectoralincomeelasticityislargerthanone,i.e.,ε >1,thatsector’s k expendituresharealsoriseswiththeincomepercapita. 5ThisisakeydifferencefromthepreferencesusedinFajgelbaumandKhandelwal(2016)andHottmanandMonarch (2018),whoseframeworkscouldbeusedtoaskasimilarquestiontoours. 11

3.2 TechnologyandMarketStructure There is a continuum of varieties, z ∈ [0,1], in both the goods (g) and services (s) sectors. The sectoralcompositegood,Q ,isanaggregateoftheindividualvarietiesQ (z): ik ik (cid:18)(cid:90) 1 η−1 (cid:19) η η −1 Q ik = Q ik (z) η dz , 0 wheretheelasticityofsubstitutionacrossvarietieswithinasectorisη >0. Eachvarietyziseither producedlocallyorimportedfromabroad. Thecompositesectoralgoodsareusedindomesticfinal consumptionanddomesticproductionasintermediateinputs: Q =C + ∑ M , ik ik ink n=g,s whereM istheintermediateinputusageofcompositegoodkintheproductionofsectorn. ink Each country possesses technologies for producing all the varieties in all sectors. Production requireslaborandintermediateinputsasinLevchenkoandZhang(2016). Theproductionfunction forvarietyz∈[0,1]insectork∈{g,s}ofcountryiis: Y ik (z)=A ik (z)(T ik L ik (z))λik (cid:2)Π n=g,s M i γ k ik n n(z) (cid:3)1−λik, (9) whereλ denotesthecountry-specificvalue-addedshareinproduction,andγ denotesthecountryik ikn specific share of intermediate inputs sourced from sector n; these parameters vary over time to track changes in input-output relationships. Y (z) denotes output, L (z) denotes labor input, and ik ik M (z) denotes sector-n composite goods used as intermediates in the production of the sector k ikn varietyz. T isthetime-varying, fundamentalproductivityofvarietiesinsectork andscalesvalue ik addedequallyacrossallvarieties. A (z)isavariety-specificproductivitylevelthatscalesgrossoutik put, which is the realization of a random variable drawn from the cumulative distribution function F(A)=Pr[Z ≤A]. FollowingEatonandKortum(2002), weassumethatF(A) isaFréchetdistribution: F(A)=e−A−θk, where θ >1. The larger is θ , the lower the heterogeneity or variance of k k A (z).6 Theparametersgoverningthedistributionofidiosyncraticproductivitydrawsareinvariant ik acrosscountriesbutdifferentacrosssectors. Weassumethattheproductivityisdrawneachperiod.7 Total sectoral labor, input usage, and production in sector k in country i are the aggregates of thevariety-levelcomponentstakenoverthesetofvarietiesproducedincountryi,V : ik (cid:90) (cid:90) (cid:90) L = L (z)dz; M = M (z)dz; Y = Y (z)dz. ik ik ikn ikn ik ik Vik Vik Vik γ 6A k (z)hasgeometricmeaneθk anditsloghasastandarddeviation π√ ,whereγisEuler’sconstant. θk 6 7Alternatively,wecouldassumethattheproductivityisdrawnonceintheinitialperiod,andastheT’schangeover time,theproductivityrelativetoT remainsconstant. 12

Goods markets are perfectly competitive; goods prices are determined by marginal costs of production. Thecostofaninputbundleinsectorkis: v =B wλik (cid:0)Π (P )γikn (cid:1)1−λik, ik ik i n=g,s in where B ik = λ i − k λik((1−λ ik )Π n=g,s γ i − kn γikn)λik−1. The cost of an input bundle is the same within a sector,butvariesacrosssectorsgivendifferentinputsharesacrosssectors. 3.3 Trade Whenvarietiesareshippedabroad,theyincurtradecosts,whichincludetariffs,transportationcosts, andotherbarrierstotrade. Wemodelthesecostsasicebergcosts,whichvaryovertimetotrackthe pattern of bilateral trade. Specifically, if one unit of variety z is shipped from country j, then 1 τijm units arrive in country i. We assume that trade costs within a country are zero, i.e., τ =τ =1. iig iis This means that the price at which country j can supply variety z in sector k to country i equals p (z) = τijkvjk. Since buyers will purchase from the cheapest source, the actual price for this ijk Tλk ik (cid:8) (cid:9)I varietyincountryiis p (z)=min p (z) . ik ijk j=1 Under the Fréchet distribution of productivities, Eaton and Kortum (2002) show that the price ofcompositegoodk∈{g,s}incountryiis: (cid:34) (cid:35)−1 P =Γ ∑ I (cid:16) T −λjkv τ (cid:17)−θk θk , (10) ik k jk jk ijk j=1 where the constant Γ k = Γ(1− η θ − k 1)1− 1 η denotes the Gamma function, and the summation term on the right-hand side summarizes country i’s access to global production technologies in sector k scaledbytherelevantunitcostsofinputsandtradecosts.8 The share of country i’s expenditure on sector-k goods from country j, π , equals the probaijk bilityofcountryiimportingsector-kgoodsfromcountry j,andisgivenby: (cid:16) T −λjkv τ (cid:17)−θk jk jk ijk π = . (11) ijk ∑ I s=1 (cid:16) T s − k λskv sk τ isk (cid:17)−θk Equation (11) shows how a higher average productivity, a lower unit cost of input bundles, and a lowertradecostincountry j translatesintoagreaterimportsharebycountryi. 8Weassumeη−1<θk tohaveawell-definedpriceindex. Underthisassumption,theparameterη,whichgoverns theelasticityofsubstitutionacrossgoodswithinasector,canbeignoredbecauseitappearsonlyintheconstanttermΓ. 13

3.4 Equilibrium Combining the goods and factor market clearing conditions and demand equations with the equations for the consumption of the composite good, trade shares, prices, and the global portfolio balanceyieldsasetofconditionsthatfullycharacterizetheequilibriumofthemodel. Table2collectsalltheseconditions. Equations(D1)-(D4)arefromthehouseholddemandside. (D1)and(D2) areoptimalconditionsforsectoralconsumptionandsectoralexpenditureshares. (D3)specifiesthe idealaggregatepriceindexgiventhepreferences. (D4)isthebudgetconstraint. Table2: Equilibriumconditions D1 C =Lωσ (cid:16) Pik (cid:17)−σ(cid:16) Ci (cid:17)εk ∀i,k ik i k Pi Li D2 e =ωσ (cid:16) Pik (cid:17)1−σ(cid:16) Ci (cid:17)εk−1 ∀i,k ik k Pi Li (cid:18) (cid:19) 1 D3 P i = (cid:16) C Li i (cid:17) ∑ k∈{g,s} ω k σ (cid:16) C Li i (cid:17)εk−σ P i 1 k −σ 1−σ ∀i D4 PC +ρwL =wL +RL ∀i i i i i i i i i (cid:18) T j − k λjkνjkτijk (cid:19)−θk S1 π = ∀i,j,k ijk ∑I s=1 (cid:16) T s − k λskνskτisk (cid:17)−θk S2 ν ik =B ik wλ i ik∏ n∈{g,s} P i ( n 1−λik )γikn ∀i,k (cid:18) (cid:19)1 S3 P ik =Γ k ∑ I j=1 (cid:16) T j − k λjkν jk τ ijk (cid:17)−θ θ ∀i,k S4 wL =λ P Y ∀i,k i ik ik ik ik S5 P M =(1−λ )γ P Y ∀i,k,n in ikn ik ikn ik ik S6 C ik +∑ n∈{g,s} M ink =Q ik ∀i,k S7 ∑ I j=1 P jk Q jk π jik =P ik Y ik ∀i,k G1 ∑ I i=1 ρ i w i L i =R∑ I i=1 L i G2 ∑ k∈{g,s} P ik Y ik −∑ k∈{g,s} P ik Q ik =ρ i L i −RL i ∀i Equations(S1)-(S7)arefromthesupplyside. (S1)givesbilateralimportsharesintotalabsorption at the sectoral level. (S2) specifies the cost of an unit of the input bundle. (S3) gives sectoral prices. (S4) and (S5) state the optimal value added and intermediate input usages implied by the Cobb-Douglasproductionfunction. (S6)linkssectoralaggregateabsorptionwithfinaldemandand intermediateinputdemand. (S7)linksacountry’stotaloutputinasectorwiththesumofalldemand fromallcountries. Equations(G1)-(G2)arefromtheglobalmarketclearing. Equation(G1)specifiesnettransfers across countries are zero globally. Equation (G2) is the resource constraint at the country level. Thesetwoconditionstogetherimplythatthegoodmarketclears. 14

We define a competitive equilibrium of our model economy with the exogenous time-varying processesforeverycountry: laborendowment{L},tradecosts{τ ,τ }I ,productivity{T ,T }, i ijg ijs i,j=1 ig is and contribution shares to the global portfolio {ρ}; time-varying structural parameters for every i country{λ ,γ };andtime-invariantstructuralparameters{σ,ε ,ω ,θ } asfollows. ik ikn k k k k=g,s Definition1. Acompetitiveequilibriumisasequenceofoutputandfactorprices{w,P ,P ,P}I , i ig is i i=1 allocations {L , L , M , M , M , M , Q , Q ,Y ,Y , e , e ,C ,C ,C}I , transfers from ig is igg igs isg iss ig is ig is ig is ig is i i=1 theglobalportfolio,R,andtradeshares{π ,π }I ,suchthateachconditionintable2holds. ijg ijs i,j=1 4 Calibration and Solution Toquantifytheroleofstructuralchangeinglobaltradeflows,wecalibratetheexogenousprocesses and parameters in the model match data from 26 countries plus one rest-of-the-world aggregate over period 1970-2015. Preference parameters, (σ,ε ,ε ,ω ,ω ), are estimated using data on secg s g s toral prices and expenditures. Processes for sectoral trade costs, τ , productivity, T , and trade ijkt ikt imbalances, ρ , are constructed to match data on sectoral value added, bilateral trade flows, and it tradedeficits. Theproductioncoefficientsλ andγ areconstructedusingtheinput-outputdata, ikt iknt andthetradeelasticity,θ ,istakenfromtheliterature. k Wewilldiscussthecalibrationproceduresindetailinthenextthreesubsections. Withthesein hand,wecansolvethebaselinemodelcompletelyinlevelsforeachyeart =1970,...,2015. 4.1 DataInputsandImputedData This subsection briefly summarizes all of the observed data and imputed data that serves as inputs tothemodel. MoredetailcanbefoundinAppendixA Laborendowment Thecountry-specific,time-varyinglaborendowment,L ,comesfromverit sion 9.0 of the Penn World Table and the World Bank’s World Development Indicator Database. Thesedatacorrespondtothenumberofworkersengagedinmarketactivity. Value added As in Section 2, we use the time series of sectoral value added—wL in our i ik model—from the United Nations Main Aggregates Database. Dividing aggregate value added by thelaborendowmentgivestheimputedwagew. i Trade Again following Section 2, we use sectoral exports and imports by country from the WIOD for the years 1995-2011, splicing with other trade data to create a longer time series. The bilateral trade data that forms the π terms are generated similarly. More detail on splice factors ijkt andotherdatasetsisinAppendixA. 15

Production shares The country-specific, time-varying production parameters, γ and λ , iknt ikt are constructed using the World Input-Output Database (WIOD), condensed down to a two-sector input-outputconstructforeachcountryfrom1995-2011. Specifically,λ istheratioofvalueadded ikt tototalproductioninsectork,whiletheγ termsaretheshareofsectork inputsthataresourced iknt from sector n. We apply the 1995 values to all years prior to 1995, similarly, we apply the 2011 valuestoallyearsafter2011. While these production shares vary quite a bit across countries, they change only mildly over time. Moreover,therearenotablepatternsthatholdacrosscountries. First,productionofservicesis morevalue-addedintensivethanproductionofgoods. Table3indicatesthat,onaverage,61percent of total service production compensates value-added factors, compared to 39 percent in goods. Second,inputsfromgoodssectorsaccountfor68ofintermediateexpendituresbythegoodssector. That is, goods production is goods-intensive. Similarly, services production is service intensive: inputs from the service sector account for 66 percent of intermediate expenditures by the service sector. Still, cross-sectorlinkagesarerelativelystrong: roughlyone-thirdofintermediateinputsin eachsectorissourcedfromtheothersector. Table3: Parametervalues Cross-country,cross-timeaverages λ Ratioofvalueaddedtogrossoutputingoods 0.39 g λ Ratioofvalueaddedtogrossoutputingoods 0.61 s γ Good’sshareinintermediatesusedbygoodssector 0.68 gg γ Good’sshareinintermediatesusedbyservicesector 0.34 sg Commonparameters σ Elasticityofsubstitutionb/wsectors 0.4 ε Elasticityofincomeingoods 1 g ε Elasticityofincomeinservices 1.59 s ω Preferencesshareofgoods 0.49 g θ Tradeelasticityingoodssector 4 g θ Tradeelasticityinservicesector 4 s η Elasticityofsubstitutionb/wvarietiesincompositegood 2 Sectoralexpenditures TheWIODprovidesdataofsectoralexpendituresfortheyears1995- 2011. Inordertorecoversectoralexpendituresfortheotheryears, somemanipulationoftheequilibriumconditionsisrequired. First,combining(S5)-(S7)yieldsthefollowingexpression: P C =P Q − ∑ (1−λ )γ (P Q +NX ), (12) ik ik ik ik in ikn in in in n={g,s} 16

where NX is net exports in country i sector k, and P Q is total absorption. From equilibrium ik ik ik conditionS4,wealsoknowtotalabsorptionofthecompositegoodcanbewrittenas: wL P Q +NX = i ik . (13) ik ik ik λ ik Usingdataonsectoralvalueadded,wL ,alongwithsectoralnetexports,NX ,andtheproduction i ik ik share,λ ,wecancalculatetotalexpenditure,P C ,viaequations(12)and(13).9 From1995-2011, ik ik ik we directly observed the sectoral final expenditures in the input-output tables so this procedure simply returns the observations. For all of the other years these data are unavailable, however, this procedure allows us to construct the sectoral expenditures in a reliable way. Once the sectoral expendituresaregenerated,theexpendituresharese arestraightforwardtocompute. ik Trade imbalances The parameters, ρ , are calibrated to match each country’s ratio of net it exportstoGDP.Inthemodel,theratioofnetexportstoGDPincountryiattimet is RtLit−ρitwitLit. In witLit thecalibrationwecanletR =0andsimplysetρ = NXit . Solongasnetexportssumtozeroacross t it GDPit countries (which it does in our data) then the global portfolio is balanced. In the counterfactual analysis,theendogenoustermR willadjusttoensurethattheglobalportfoliobalancesperiod-byt period: R t∑ I i=1 L it =∑ I i=1 ρ it w it L it . 4.2 CommonParameters Preferenceparameters Ourestimationofpreferenceparametersusesdataonsectoralprices, sectoralexpenditureshares,andemploymentlevels.10 Takingtheratioofequation(8)asitapplies toeachsectorwecanshow: (cid:18) e (cid:19) (cid:18) ω (cid:19)σ(cid:18) P (cid:19)1−σ(cid:18) C (cid:19)εg−εs ig g ig i = , e ω P L is s is i whichillustratestheintuition. Holdingfixedvariationintotalconsumption(incomeeffects),theextentthatexpendituresharesmovewithrelativepriceshelpsusidentifytheelasticityofsubstitution, σ. Holding fixed relative prices, the extent that expenditures shares move with the aggregate level of consumption helps us identify income elasticities, ε . By setting the sector weights, ω , to be k k constantacrosscountriesandovertimeallowsustoexploitboththecross-sectionalandtime-series variationtoidentifythepriceandincomeelasticities. Weestimatethepreferenceparametersω ,ω ,σ,ε tominimizethesumofthesquareddeviation g s s 9Equations (12) and (13) exactly summarize how we constructed sectoral expenditure for the empirical results in Section2,andisdetailedinwordsinSection2.1andFigure1. 10Ourdataongross-outputsectoralpricescomesfromtheUnitedNationsMainAggregatesDatabaseandtheGGDC ProductivityLevelDeflator,asdetailedinAppendixA.Thesepricesareonlyusedforestimatingthepreferenceparameters;wewillsolveformodel-consistentpricesinSection4.3. 17

of relative sectoral expenditure shares between the model and the data. Specifically, we solve the constrainedminimizationproblem: min 2 ∑ 015 ∑ I   (cid:18) ω g (cid:19)σ (cid:32) P(cid:99)igt (cid:33)1−σ(cid:18) C it (cid:19)εg−εs − (cid:18) e (cid:99)igt (cid:19)   2 (14) ωg,ωs,σ,εst=1970i=1 ω s P(cid:99)ist L(cid:99)it e (cid:99)ist s.t. P (cid:91) it C it = (cid:32) ∑ ω k σ (cid:18) C it (cid:19)εk−σ P(cid:99)ikt 1−σ (cid:33) 1− 1 σ ,∀(i,t) (15) L(cid:99)it k∈{g,s} L(cid:99)it ∑ ω =1, (16) k k∈{g,s} where hats on variables indicate that the objects come from data. That is, we use data on sectoral prices, P(cid:99)ik , sectoral expenditure shares, e (cid:99)ik , aggregate expenditures, P(cid:100)i C i , and employment levels, L(cid:98)i . Wehavenodirectempiricalcounterparttotheaggregateconsumptionindex,C i ,asitisdefined in the model, so the constraint in the optimization problem allows us to pin this object down in a model-consistent way by internally deflating the aggregate expenditures by an appropriate price deflator. Ourproceduretosolvetheminimizationproblemisasfollows. Firstwenormalizetheincome elasticity for goods ε ≡1 as in Comin et al. (2015). Second, we make a guess for the remaing ing preference parameters: (ω ,ω ,σ,ε ) . Third, given these parameter guesses, we solve for the g s s internally consistent aggregate consumption index, C , for each country in every year using conit straint (15), which is a simple nonlinear equation with one unknown. Fourth, given the imputed consumption indexes and the data discussed above, we use nonlinear least squares on the objective function (14) to obtain updated estimates of (ω ,ω ,σ,ε ). With the updated estimates of the g s s preference parameters, we impute updated consumption indexes and, in turn, new estimates of the preferenceparameters. Wecontinuetheprocedureuntilconvergingtoafixedpointinthepreference parameters. Theresultoftheestimationdeliversσ =0.4andε =1.59. Theω parametersemergeduring s k the estimation; we normalize prices such that ω =0.49 —the world expenditure share on goods g in 1970. Implicitly we also obtain estimates of the aggregate consumption index, C , which has it no direct empirical counterpart. This object will be used later on in order to calibrate productivity levelsinaninternallyconsistentmanner. Othercommon parameters Thelower paneloftable3 providesthevalues forcommonparameters. We set θ =4 following Simonovska and Waugh (2014). There is no reliable estimate g of the trade elasticity for services, so we set θ =4 as well. The elasticity of substitution between s varieties in the composite good, η, plays no quantitative role in the model other than satisfying 1+(1−η)/θ >0;wesetthisvalueat2. 18

4.3 TechnologyandTradeCosts We recover the productivity terms, T , and trade costs, τ , by exploiting structural relationships ik ijk from our model in order to match data on sectoral final expenditures and bilateral trade flows in each country and every year. Our procedure is similar to that of S´wie˛cki (2017), but incorporates input-output linkages as in Sposi (2016). By explicitly making use of the observed input-output linkages,ourprocedurealsoimpliesthatwesimultaneouslymatchsectoralvalueadded. Twokeystructuralrelationshipsprovideidentificationforproductivityandtradecosts: B ν Tλik = ikt ikt , (17) ik Γ− k 1P ik (π iik ) − θ 1 k τ = (cid:18) π ijk (cid:19)− θ 1 k (cid:18) P ik (cid:19) . (18) ijk π P jjk jk Bothstructuralrelationshipsarederivedbymanipulatingequations(10)and(11). Measurementof sectoralproductivitytakesintoaccountdifferencesbetweenimputedinputcostsandimputedoutput prices. Holding fixed the unit costs of inputs, the model assigns a high productivity to a country with a low price, meaning that inputs are converted to output at an efficient rate. It also takes into accountthehometradeshare,whichreflectstheselectioneffectcommontoRicardiantrademodels. Measurement of the trade costs takes into account relative imputed price differences and the bilateral trade shares. Holding fixed the imputed price difference between countries i and j, if country i imports a large share from country j relative to what j sources from itself, the inferred trade barrier is low. In this sense, the trade costs are treated as wedges that reconcile the observed patternofbilateraltrade. Inferring internally consistent prices Equations (17) and (18) require data on units costs, sectoral prices, and trade shares; unit costs themselves require wages and sectoral prices. While we have observed data on prices, we do not use them for this part of the calibration. Instead, we imputesectoralpricesthroughthelensofthemodelsothattheyareinternallyconsistentwithsector expenditures. Our model does not have enough degrees of freedom to match both sectoral prices andsectoralexpendituressimultaneously,sowechoosetomatchexpendituressincetheyareoffirst orderinteresttoourquestion. Inotherwords,giventhesectoralexpendituresanddataonconsumption levels, we recover the sectoral prices that support the expenditures using the representative household’sfirst-orderconditions. Specifically,givenpreferenceparameters,(ω ,ω ,σ,ε ,ε ),sectoralexpenditures,P C ,labor g s g g ik ik endowment, L, and the estimated levels of aggregate consumption, C (obtained from estimating i i preferenceparameters),weinvertthehousehold’sfirst-ordercondition(8)andusethedefinitionof aggregateexpenditures(7)torecovermodel-impliedpricelevelsthatsupporttheexpenditures. 19

With these constructed sectoral prices in hand, we compute the sectoral productivity and trade costsinequations(17)and(18). Figure5illustratesthecalibratedprocessesattheworldlevel. The left panel plots the global sectoral productivity growth index. The global sectoral productivity is computedastheaverageacrosscountriesweightedbyeachcountry’sshareinsectoralvalueadded. Theindexistakenrelativeto1970andisreportedinlogs. Asshowninthefigure,theglobalsectoral productivitygrowsfasteringoodsthaninservices. Figure5: Calibratedglobalproductivityandtradecosts Log index of productivity Sectoral trade barriers 6 6 Goods Goods 5 Services 5 Services 4 4 3 3 2 1 2 0 1 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 TherightpanelofFigure5plotstheglobaltradecostsforgoodsandservices. Theglobaltrade costiscomputedasanaverageofallbilateraltradecostsweightedbythebilateraltradeflows. As illustratedinthefigure,tradecostsforbothgoodsandservicesdeclineovertime,andtradecostsin services are higher than those in goods, in general. This completes the description of the baseline modelequilibrium. 4.4 ModelFit Our calibration procedure ensures that the model fits data on sectoral value added, sectoral gross output, sectoral absorption, sectoral bilateral trade flows, and sectoral expenditures. In order to rationalizethesectoralexpendituresunderourpreferencespecification,thesetofequilibriumprices differ from those in the data. Alternatively, one could force the model to match the observed price data, but then the model would not match the sectoral expenditures due to the limited degrees of freedom in the preference specification. We opt to match expenditures since the sectoral ratios of tradetoexpenditureareoffirst-orderinterestinourcounterfactuals. Nonetheless, we can compare the prices generated by the model to those in the data as a test of fit. This is illustrated in figure 6; all prices are taken relative to the U.S. in 2015. Each point correspondstothepriceinonecountryinoneyear. Thepricesofservicesfitthedataverywell;the correlationbetweenmodelanddatais0.96. Thepricevariationforgoodsinthemodelisoverstated 20

relativetothatinthedata,butthecorrelationseemsquitereasonable: 0.69. Figure6: Sectoralprices: modelversusdata,inlogs,relativetotheU.S.in2015 Goods Services 4 2 3 le le d d o M 2 o M 1 :e c irP 1 :e c irP 0 0 45o -1 45o -1 -1 0 1 2 3 4 -1 0 1 2 Price: Data Price: Data 5 Model-based Counterfactuals This section quantitatively assesses the role of structural change on global trade volumes by conducting counterfactuals using the calibrated model. We also highlight the importance of structural changeonmodel-basedmeasuresoftradecostsandwelfaregainsfromtrade. 5.1 GlobalTradeintheAbsenceofStructuralChange To examine the implications on global trade flows from structural change, we construct a counterfactual in which structural change is absent by restricting expenditure shares to be constant over time. This provides the closest model-based analog to our reduced-form counterfactual in Section 2. Todoso,weassumethatthepreferencesinthecounterfactualaregivenby: C = ∏ C ω i (cid:48) k. (19) i ik k∈{g,s} WiththeCobb-Douglasspecification,theincomeelasticitiesare1forbothsectorsandthesubstitution elasticity is also 1 across the two sectors. Consequently, the expenditure shares across sectors areconstantovertime. Thatis: e =e =ω(cid:48) . (20) ikt ik0 ik All underlying processes in the counterfactual are identical to those in the baseline. To be morespecific,inthecounterfactualweassumeallotherparametersandtimevaryingprocessesfor T, τ, and L are unchanged from the baseline, except that the preference parameters {σ,ε ,ω } in k k 21

the baseline are set to {1,1,ω(cid:48) } in the counterfactual experiment. That is, prices and trad flows ik still evolve endogenously over time. We choose values for ω(cid:48) =e so that in 1970 the sectoral ik ik0 expendituresharesareidenticaltothoseinthebaselinemodel. Wecomputetheequilibriumforthecounterfactualexperimentandanalyzehowtheabsenceof structuralchangeimpactsglobaltradeflows. OursolutionprocedureisbasedonAlvarezandLucas (2007). Start with an initial guess for the vector of wages. Given the wages, recover all remaining prices and quantities across countries using optimality conditions and market clearing conditions, excluding the trade balance condition. Then use departures from the trade balance condition to update the wages. Iterate on wages until the trade balance condition holds. The exact details are availableinAppendixB. 5.1.1 Modelcounterfactualresults Westartbyhighlightingthedrivingforceofthecounterfactualinfigure7. Inthedataandbaseline model, the goods share of total expenditure falls from about 50 in 1970 percent to 20 percent in 2015,asillustratedbythesolidline. Inthecounterfactual,thegoodsexpenditureshareisheldfixed at its initial value, country-by-country. When aggregated to a global expenditure share, it remains close to 50 percent over time, increasing somewhat near the end of the sample, as shown by the dashedline. Theslightrisesince2002isdrivenbytheincreasingweightofChinaandIndiainthe worldeconomy, bothofwhichhavelargerexpendituresharesingoodscomparedtothedeveloped countries. Figure7: Goodsexpenditureshares,baselineandcounterfactual 0.8 Baseline Fixed expenditure shares 0.7 0.6 0.5 0.4 0.3 0.2 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 We next present the implications for global trade flows. Figure 8 compares openness between themodelbaseline(solidline),modelcounterfactual(dashedline),andreduced-formcounterfactual (dotted line). In both counterfactuals, global trade would have been much higher had structural 22

change not occurred. By 2015, the reduced-form counterfactual puts openness at 91 percent while themodelcounterfactualputsitat68percent,comparedwith45percentinthedata. Thedifference betweenthetwocounterfactualspeaksin2015andisdrivenbytheendogenouschangestosectoral opennessgeneratedbythemodel.11 Figure8: Openness: baselineandcounterfactuals 1.2 Baseline Fixed expenditure shares, model 1 Fixed expenditure weights, empirical 0.8 0.6 0.4 0.2 0 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 5.1.2 Quantitativemechanisms Themotivationforourmodelofstructuralchangeistheabilityofthemodeltodeliveranalternate path for sectoral openness that responds to the same forces that drive structural change. Figure 9 shows sectoral openness in the model counterfactual compared with observed sectoral openness (whichboththemodelbaselineandthereduced-formcounterfactualuse). Theleftpanelshowsthat goodsopenness(theratioofgoodstradetogoodsexpenditure)isabout70percentagepointslower relativetothebaselinein2015,whileservicesopennessisabout5percentagepointshigher. Tounderstandhowsectoralopennessendogenouslyrespondstochangesinexpendituresharesin themodel,wedecomposesectoraltradeopennessintotwoterms: (i)theratiooftradetoabsorption and(ii)theratioofabsorptiontoexpenditure: (cid:18) (cid:19) (cid:18) (cid:19) Trade Trade Abs kt = kt × kt . (21) Exp Abs Exp kt kt kt Thesetwotermscorrespondtotwopotentialchannelsofbiasinherentinthereduced-formcounterfactual. Throughendogenousgeneralequilibriumeffects, changingsectoraldemandmightchange the relative wages across countries, and thus the ratio of trade to absorption, which is captured by 11AppendixCshowsstructuralchangeandthemodel-basedcounterfactualforeachsamplecountryinfigure18and 19respectively,aswellasadecompositionofeachcountry’scontributiontotheaggregatecounterfactualintable4for 2015. 23

thefirstterm. Inthemodel,atthecountrylevel,thefirsttermissimilarto1−π foreachcountry iik i and sector k.12 Also, changing the sectoral demand shares might affect the ratio of absorption to expenditurethroughinput-outputlinkages,capturedbythesecondterm. Figure9: Sectoralopenness: baselineandmodelcounterfactual Goods Services 0.25 Baseline Baseline 2 Fixed expenditure shares 0.2 Fixed expenditure shares 1.5 0.15 1 0.1 0.5 0.05 0 0 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 We now quantify the bias of each channel. The ratios of trade to absorption in each sector are almost identical in the baseline and in the counterfactual, as shown in the upper panel of figure 10. Recall the expression of π in equation (S1) in table 2. Since the productivity and the trade iik costprocessesareunchanged,theonlywaythatchangingexpenditurepatternsaffectthetrade-overabsorptionratiosisthroughitsimpactonrelativewagesacrosscountries. Itturnsoutthatthegeneral equilibrium effect on relative wages is quantitatively small in the model counterfactual. Thus, the share of each country’s absorption that is sourced from abroad in each sector barely changes from thebaselinetothecounterfactual. The primary reason why sectoral trade openness in the model counterfactual differs from the baselineisduetodifferencesintheratioofabsorptiontoexpenditure,asshowninthelowerpanel offigure10. Theratiosofabsorptiontoexpenditureinthecounterfactualrisebylessovertimefor the goods sector, but rise by more over time for the services sector, compared with the baseline. Using the expression of sectoral absorption in equation (S6) of table 2, we can write the sectoral ratioofabsorptiontoexpenditureas: Q C +M +M Q C +M +M ig ig igg isg is is igs iss = , = , C C C C ig ig is is wheresectoralabsorptionequalsfinalplusintermediatedemandforthesectoralcompositegood. In order to counterfactually increase consumption of goods,C , intermediates must be sourced from ig both sectors, implying that M and M rise, since these are directly used to produce the greater igg igs 12Sectoral imports over expenditure is exactly equal to 1−πiik . Sectoral exports differ, but quantitatively they are highlycorrelatedwithsectoralimportsacrosscountries. 24

Figure10: Sectoraltradeoverabsorption,sectoralabsorptionoverexpenditure Goods Services 0.14 n o itp 0.8 B Fi a x s e e d l in e e xpenditure shares n o itp 0.12 B Fi a x s e e d l in e e xpenditure shares ro ro s0.6 s 0.1 b b a a re re0.08 v0.4 v o o e e0.06 d d a rT 0.2 a rT0.04 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Goods Services e5 e2.4 ru ru tid Baseline tid Baseline n Fixed expenditure shares n2.2 Fixed expenditure shares e e p x4 p x e e re re 2 v v o o n3 n1.8 o o itp itp ro ro1.6 s s b2 b A A 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 demand for goods consumption. At the same time, derived demand for M and M decline in isg iss response to a decline inC . Consequently, absorption rises by less than expenditure in the goods is sector,whileabsorptiondeclinesbylessthanexpenditureintheservicessector,implyinglower Qig Cig andhigher Qis inthemodelcounterfactualcomparedwiththebaseline. Cis Goingbacktofigure9,weconcludethatalthoughservicestradeopennessgoesup,goodsopennessdecreasessufficientlytoimplyaloweroveralltradeopennessinthemodelcounterfactualthan in the empirical counterfactual. This major bias of the reduced-form counterfactual in predicting globaltradeopennessintheabsenceofstructuralchangecomesfromignoringinput-outputlinkages acrosssectors. To confirm the importance of input-output linkages, we recalibrate the baseline model and the corresponding counterfactual in a world with no input-output linkages (γ = γ = 1).13 In this gg ss world, the absence of structural change in the model counterfactual implies little deviation in sectoraltradeopennessfromthebaseline/data. Ascanbeseeninfigure11,thesectoralratiosoftrade to expenditure barely change from the baseline to the counterfactual. Also, the sectoral ratios of absorption to expenditure barely change either. In other words, in the model with no intersectoral linkages,themodelcounterfactualyieldsthesamepredictionasthereduced-formcounterfactual. 13Thisrecalibrationrequiresamanipulationofsectoralexpendituresusingequations(12)and(13)toensurethatthe modelmatchesthesectoralvalueaddedandsectoralnetexportsasinthedataandthenationalaccountingidentityholds. 25

Figure11: Sectoraltradeoverabsorption,sectoralabsorptionoverexpenditure: γ =γ =1 gg ss Goods Services 0.12 n o0.8 No IO n o No IO itp No IO, fixed expenditure shares itp 0.1 No IO, fixed expenditure shares ro ro s0.6 s b a b a0.08 re re v0.4 v o o0.06 e e d d a rT 0.2 a rT 0.04 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Goods Services e5 e2.4 ru ru tid No IO tid No IO n No IO, fixed expenditure shares n2.2 No IO, fixed expenditure shares e e p x4 p x e e re re 2 v v o o n3 n1.8 o o itp itp ro ro1.6 s s b2 b A A 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 5.1.3 Decomposingincomeversussubstitutioneffects The literature on structural change has established two key mechanisms: income effects and substitution effects. Boppart (2014) provides the first model that incorporates both income and substitution effects to generate structural transformation along a balanced growth path. Herrendorf, Rogerson and Valentinyi (2013) demonstrate that when structural change is defined over final expenditures instead of value added, as it is in our paper, then income effects play a nontrivial role relativetosubstitutioneffects. We use our model to evaluate the relative importance of each effect in shaping global trade flows. In our model counterfactual, we set ε =1 so that preferences are homothetic, i.e., income s elasticity of demand in each sector equals 1.14 By comparing global trade openness implied by thisexperimentwiththatofthecounterfactualwithbotheffectsshutoff,wecanseetowhatextent the income effect drives our results. Alternatively, the comparison will illustrate the power of the substitutioneffectalone. Figure12plotstheworldratiooftradetoexpenditureimpliedbyourmodelcounterfactualwithouttheincomeeffect,depictedwiththedottedline. Forcomparison,wealsoplottradeopennessin thedatawiththesolidlineandtheoneimpliedbyourmodelcounterfactualwithouttheincomeand 14Weadjustthepreferencesweights,ωik ,sothatin1970thesectoralexpendituresareidenticaltothoseinthebaseline model. 26

substitutioneffectwiththedashedline. Ascanbeseeninthefigure,themodelthatshutsdownthe incomeeffectleadstoaratiooftradetoexpenditureabout10percentagepointshigherthanthedata, oraboutone-fourthofthedifferencebetweenthedataandthefixed-expenditure-sharescounterfactual. Thus,theincomeeffect’scontributiontostructuralchangeaffectsinternationaltradeoverthis timeperiod,butthesubstitutioneffect’scontributionisgreater. Figure12: Openness: baseline,modelcounterfactual,andno-income-effectcounterfactual(ε =1) 1.2 Data Fixed expenditure shares 1 No income effects 0.8 0.6 0.4 0.2 0 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 Year 5.2 GlobalTradeintheAbsenceofDecliningTradeCosts Arguably,decliningtradecostsisthemostcommonfactorattributedtotheriseinglobalopenness. Indeed, the past few decades have witnessed drastic reductions in shipping costs and in tariffs. To examine the role of declining trade barriers, consider a counterfactual in the model where trade barriersareheldattheir1970levels. Theresultingtradeopennessisillustratedbythedottedlinein figure13. Inthisworld,theglobalratiooftradetoexpenditurebarelygrowsatall. Ofcourse,trade costs in the baseline model are calculated as the residuals required to account for changes in trade notdrivenbytechnologyordemand. Assuch,theyincorporateawidevarietyofeconomicforces, includingtariffreductions,improvementsinshippingtechnology,orevencompositionalchangesin demandatafinerlevelofdisaggregationthanourgoodsandservicesdistinction. Thatsaid,theconstant-trade-costcounterfactualalsodemonstratesthequantitativesignificance of structural change on global trade openness. As shown in figure 13, structural change has held backtradebyroughlythesamemagnitudethatreductionsintradecostshaveboostedtradeoverthe pastfourdecades. 27

Figure13: Openness: baseline,modelcounterfactual,andconstant-trade-costcounterfactual e ru tid Baseline n0.9 e Fixed expenditure weights p x e0.8 Constant trade costs la n0.7 if d lro 0.6 w o0.5 t e d0.4 a rt d0.3 lro W0.2 :o ita0.1 R 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 Year 5.3 ImportanceofStructuralChangeinTradeModels Sofarwehaveemphasizedhowtheprocessofstructuralchangerestrictstheprogressintradeopennessovertime,asmeasuredbytheratiooftradetoexpenditure(ortradetoGDP).Aprominentforce isthatascountriesconsumerelativelymoreservices,whicharetradedlessintensivelythangoods, globaltradevolumesarerestricted. Thetradeliteraturereliesheavilyoninterpretingobservedtrade volumes through the lens of a model to estimate trade costs and welfare gains from trade. An immediate corollary of our findings is that incorporating structural change in the model is important fortheseestimates. Thegoalofthissubsectionistoelaborateonthispoint. 5.3.1 Structuralchangeandtradecosts Consider a standard one-sector model analogous to our baseline two-sector model. There is one composite good, constructed from a continuum of tradable varieties, and used as an intermediate inputbyafirmorasafinalconsumptionbythehousehold. Thehousehold’spreferencesaredefined only over consumption of the composite good. Structural change is absent by construction in this model. We calibrate trade costs using a structural equation similar to equation (18) in the two-sector model,butuseaggregatepricelevelsandaggregatetradeshares: (cid:18) π ij (cid:19)− θ 1 (cid:18) P i (cid:19) τ = . (22) ij π P jj j Wecontrasttheestimatesoftradecostsinaone-sectormodelwiththoseinthetwo-sectormodel in figure 14. The aggregate trade barrier in the one-sector model is plotted as a dashed line, while the trade-weighted aggregate from the sectoral barriers in the two-sector model are depicted in a 28

dotted line.15 The estimated trade barrier declines by less in the one-sector model than the tradeweighted aggregate from the two-sector model, although both estimates target the same observed trade flows. The key reason is that in the absence of structural change, which dampens openness, the estimated trade barrier need not decline by much to rationalize the observed trade flows in the one-sectormodel. Figure14: Modelbasedestimatesoftradebarriers 5.5 Goods Services 5 Trade-weighted average s re One sector-calibration irra 4.5 b e d a 4 rt la ro3.5 tc e S 3 2.5 1970 1980 1990 2000 2010 Year The period 1980-2000 particularly highlights the bias in trade cost estimates when ignoring structural change. Figure 14 shows rising trade cost starting in 1980; they stay high until 2000 in the one-sector model, while costs decline by about 5 percent in the two-sector model. The reason behindthisdifferenceisthatinthisperiod, thespeedofstructuralchangeisfast, whilethegrowth of trade openness is slow, as shown in figure 2. To capture the muted growth in trade openness during these two decades, the one-sector model ignores the dampening effect of structural change, requiring rising trade costs. The two-sector model, in contrast, accounts for the fact that structural changeisholdingbacktradeflows,thusdeliveringcontinueddeclinesingoodstradebarriers. This isconsistentwiththeongoingtradeintegrationprocessesinthegoodssectorovertheseyears. 5.3.2 Structuralchangeandthegainsfromtrade Just as structural change impacts model-based estimates of the level and path of trade barriers, the same is true for estimates of the gains from trade. Welfare gains from trade are defined as world consumption(thesumofconsumptionlevelsacrosscountries)inthebaselinerelativetothatunder autarkyineveryyear,whichwecalculateforboththeone-sectormodelandtwo-sectormodel. For the two-sector model, aggregate consumption in each country is given implicitly by equation (4). 15Recallthattheworld-levelbarrieristheaverageofallcountry-levelbilateraltradebarriersweightedbythebilateral tradeflows. 29

Bothmodelsmatchobservedopennessineverycountryandeveryyear.16 Thegainsintheone-sectormodelareillustratedbythedashedline,andthoseinthetwo-sector modelareillustratedbythesolidlineinfigure15. Therearetwosignificantfindingsfromthefigure. First, there are systematic level differences: welfare gains relative to autarky are always greater in the one-sector model than in the two-sector model. Second, there is a systematic slope difference: overtime,thegainsfromtradeincreasebyfarmoreintheone-sectormodelthaninthetwo-sector modelovertime. Wediscusseachoftheseresultsinturn. Figure15: Globalgainsfromtrade y 1.1 k ra Baseline two-sector model tu Modified baseline one-sector model a o 1.08 t e v ita1.06 le r e n ile1.04 s a b n i "1.02 C " d lro W 1 1970 1980 1990 2000 2010 Year Thelevelofwelfaregains Thefactthatthegainsfromtradearelowerinthetwo-sectormodel isstartling,giventhatmuchoftheliteraturehasfoundthatestimatedgainsfromtradeincreasewith thenumberofsectors(e.g.CostinotandRodríguez-Clare2014). Whydowefindthis? Throughout this paper, we have described structural change as the shift in sectoral expenditure patterns over time and built a model where those sectoral expenditure shares are endogenous outcomes. Importantly,however,amodelthatincorporatesstructuralchangewillalsoimplychanging expenditure shares as a country shifts from autarky to trade. By contrast, constant expenditure sharesareacommonassumptionoftheexistingliteratureonwelfaregainsfromtrade. Inourmodel, lower trade costs imply a lower relative price of goods and higher income, both of which result in lowerexpenditureongoodsrelativetoservices. Thisshiftinexpendituresharesimpedesthegains fromtraderelativetoaone-sectormodel. To drive home this point, consider a simplified version of our model with no intermediates and Cobb-Douglas preferences, common to the bulk of the existing literature. For a two-sector model with exogenous sectoral expenditure shares, ω , let aggregate real consumption with trade kt 16Yilmazkuday (2018) estimates gains from trade using non-homothetic preferences, in particular, normalized CES preferencesinonelayerofaggregationacrosssourcecountries. 30

be written asC2S =C ωigtCωist, and similarly, aggregate consumption without international trade as it igt ist C˜2S =C˜ωigtC˜ωist. Thegainsfromtradeare: it igt ist C2S (cid:18) C (cid:19)ωigt (cid:18) C (cid:19)ωist G2S≡ it = igt ist . (23) it C˜2S C˜ C˜ it igt ist That is, the aggregate gains are a weighted average of the “sectoral” consumption gains, with weightsgivenbythesectoralexpenditureshares. Withthesepreferencesandourproductionsetup,asshowninArkolakis,CostinotandRodríguez- Clare(2012)andCostinotandRodríguez-Clare(2014),thewaysectoralconsumptionchangeswhen acountryopenstotradeisdirectlylinkedtotheobservedsectoralhometradeshares,π . Inother iikt words,equation(23)canbewrittenas: G2S = (cid:18) π − θ 1 (cid:19)ωigt (cid:18) π − θ 1 (cid:19)ωist = (cid:16) π ωigtπωist (cid:17)− θ 1 . (24) it iigt iist iigt iist Since in the data, the goods home trade share is less than the services home trade share, goods consumptionrisesbymorethanservicesconsumptionwhenacountryopenstotrade. Inaanalogousone-sectormodel,thegainsaresummarizedbytheaggregatehometradeshare: G1 it S =(π iit )− θ 1 =(ω igt π iigt +ω ist π iist )− θ 1 , (25) wherethe thirdexpression makesuseof thefact thatthe aggregatehometrade shareis aweighted average of sectoral expenditure shares, since we are assuming no intermediate inputs. Comparing equations (24) and (25), Jensen’s inequality means that the two-sector gains must exceed the onesector gains, which is the typical result. A similar argument was made by Levchenko and Zhang (2014).17 However, in our model, the expenditure shares are endogenous, driven in particular by prices and total expenditure, which in turn depend on our estimates of the vector of trade costs τ and the vector of productivity parameters T.18 A version of the above preferences that incorporates the endogeneityofexpendituresharesisC2S =C Eigt(τ,T) C Eist(τ,T) ,andC˜2S =C˜Eigt(∞,T) C˜Eist(∞,T) ,where it igt ist it igt ist E istheexpenditureshareonsectork andτ →∞representsautarky.19 Welfaregainsusingthese ikt 17Thisresultreliesonassumingaggregatetradebalance. 18Recallthatourexpressionforserviceexpenditureshare(fromequation8)isgivenby: P C (cid:18)P (cid:19)1−σ(cid:18)C (cid:19)εs−1 e is = P is C is =ω s σ P is L i . i i i i 19UsingthesepreferencesmeansthatwelfaregainswillnotbedirectlycomparabletotheCobb-Douglaspreferences withexogenousexpendituresharesbecausetheimpliedlevelofautarkyconsumptionwillbedifferent. Thusthecomparisonstothetwo-sectormodelwithexogenouspreferencesismainlyforintuitionaboutwhyourfullyspecifiedmodel deliverslowergains. 31

preferencescanbewrittenas: (cid:34) (cid:35)(cid:34) (cid:35) G2S≡ C i 2 t S = (cid:18) C igt (cid:19)Eigt(τ,T) (cid:0) C˜ (cid:1)Eigt(τ,T)−Eigt(∞,T) (cid:18) C ist (cid:19)Eist(τ,T) (cid:0) C˜ (cid:1)Eist(τ,T)−Eist(∞,T) it C˜2S C˜ igt C˜ ist it igt ist (cid:18) C (cid:19)Eigt(τ,T)(cid:18) C (cid:19)Eist(τ,T)(cid:18) C˜ (cid:19)Eigt(τ,T)−Eigt(∞,T) igt ist igt = , (26) C˜ C˜ C˜ igt ist ist wherethelastequalitycomesfromthefactthattheexpendituresharesmustsumto1. Becausethe expenditure shares are equilibrium allocations, rather than parameters, the exercise of comparing utilityacrosstheautarkyandtradingenvironmentsremainsvalid. Note from the last equality that the aggregate welfare gains can be separated into the sectoral gains, which are of the same format as equation (23), multiplied by a factor that accounts for the endogenous response in expenditure shares, E (τ,T)−E (∞,T). What happens to the expenigt igt diture shares when a country goes from autarky to open trade? In our model, opening up to trade reduces the relative price of goods and raises income, both generating a decline in the goods expenditureshare(i.e. E (τ,T)<E (∞,T)). Figure16demonstratesthisresultbycomparingthe igt igt goods expenditure shares in our model between autarky and free trade. The figure, using 2010 as anexample,demonstratesthatthemodel-impliedexpenditureshareongoodstendstofallbyabout 3percentagepointsonaveragewhenacountrymovesfromautarkytotrade. Thus,inourmodelofstructuralchange,thecontributiontogainsfromtradecomingfromgoods consumption is lower than the standard two-sector model because of the lower weight attached to goodsconsumptioninthetradingequilibrium.20 Empirically,thegoodssectorismostimportantfor thegainsfromtrade(sinceitismoreopen),hence,ourmodelimpliessmalleraggregategainsfrom trade compared to a model with fixed expenditure shares. These reduced gains from endogenous expendituresharesissufficienttooverturnthestandardresultthatmulti-sectormodelshavegreater gainsfromtradecomparedtoanequivalentone-sectormodel.21 The path of welfare gains Returning to figure 15, it is clear that our model also delivers lower growth in the gains from trade over time compared to a one-sector model. Similar logic as abovecarriesthroughtoconsiderthetimeseriespathofwelfaregains: asstructuralchangeoccurs, captured by declining goods expenditure share, global openness is suppressed since less-traded services,becomemoreprominent. Mechanically,sincetheweightontheserviceshometradeshare rises over time, the gains are lower compared to a world without structural change, i.e., constant expenditureshares. 20Thiscanalsobeseenbycomparingthefirstequalityofequation(26)toequation(23),withtheconditionthatthe equilibriumexpenditureshareongoodsunderinternationaltradefrom(26)matchthedata(whichholdsforus). 21The one-sector model expressions for gains, equation (25), is unchanged by considering endogenous expenditure shares,sincetherearenoexpenditureshares. However,comparingequations(25)and(26),Jensen’sInequalityclearly nolongerholds. 32

Figure16: Goodsexpendituresharesin2010: Tradeversusautarky BRA JPN 25 IRL USA IDN CHN AUS 20 ROW IND TUR ESP FIN y r15 CAN tn u ITA o GRC C GBR FRA 10 KOR MEX CYP DNK PRT 5 SWE NLD DEU AUT BLX 0 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 Difference in good's expenditure share: e -ea ig ig Connectingincomedifferencestogainsfromtradethroughstructuralchange Thisanalysis also implies that a country’s level of economic development is indicative of its gains from trade. That is, emerging economies tend to have higher goods expenditure shares than advanced economies. Thismeansthat,evenwiththesamehometradeshares,emergingeconomieswilltend tohavegreatergainsfromtradethanadvancedeconomies. 5.4 ProjectingtheFutureImpactofStructuralChangeonTrade Therecentslowdowninthegrowthofinternationaltradehaspromptedcarefulconsiderationofthe forces that might be restraining trade or no longer boosting it (IMF 2016b, Lewis and Monarch 2016). Whilestructuralchangehasnotbeenastrongerdragontradegrowthrecentlythanitwasin preceding decades, world trade as a share of total expenditure is likely to fall in the future absent additionaltradecostreductions. We show this possibility quantitatively through the lens of our model. Specifically, we extrapolate our sample of countries holding trade costs fixed at their 2015 value and letting goods and 33

services productivity grow at their respective world average rates observed between 1970-2015.22 Without additional factors boosting trade, our model implies that the ratio of trade to expenditure wouldfallfrom45percentin2015to37percentin2035,showninfigure17. Figure17: Openness: projection 0.7 0.6 0.5 0.4 0.3 0.2 0.1 1970 1980 1990 2000 2010 2020 2030 Thisquantitativeexamplehighlightstheimportanceofpayingattentiontotheroleoftheprevalent process of structural change when considering trade flows. Without incorporating structural changeintothemodel, thedownwardpatternintheratiooftradetoGDPfromfigure17wouldbe attributed to rising trade costs. However, we find such a result even without any change in trade costs, as the effects of increased services consumption in a world without rapid trade growth materially affects the trajectory of global trade openness. In other words, it is perfectly within reason to imagine a decline in the ratio of trade to GDP, or even a decline in total trade flows, without anyincreasedtradebarriers. Allthatwouldbenecessaryisthecombinationofongoingchangesin services consumption along the lines of that seen in the past four decades with the continuation of currentlevelsoftradebarriers. 6 Conclusion We show that structural change, in which the world is consuming an ever greater share of total incomeonservicesrelativetogoods,hasexertedasignificantdragonglobaltradegrowthoverthe pastfourdecades. Intheabsenceofstructuralchange,definedasfixingexpendituresharesingoods and services at their 1970 level, the global ratio of trade to GDP would be 23 percentage points higher,or71percenthigher,thaninthedata. Thisisaboutthesamemagnitudethatdecliningtrade costshavecontributedtotheincreaseinglobalopennessoverthesameperiod. 22Goodsproductivitygrows14.1percentandservicesgrows1.1percentannually. 34

We quantify the implication of structural change on global trade with a general-equilibrium modelincorporatingcomparativeadvantage,non-homotheticpreferences,andaninput-outputstructure. Themodelhighlightsthatsectoralopennessisendogenous,andthatholdingexpendituresfixed at their 1970s levels would have resulted in lower goods openness through the presence of inputoutputlinkages. Ontheotherhand, hadstructuralchangenotoccurred, aggregateopennesswould have been higher, as goods openness is much greater than services openness. The model also impliesthatincomeeffectsaloneaccountforaboutone-quarteroftheeffectstructuralchangehashad ontradevolumes. We also show that with structural change and endogenous expenditure shares, a two-sector model can imply lower gains from trade than a one-sector model, in contrast to similar models withoutstructuralchange. Commontomostmodelsofinternationaltrade,astradebarriersdecline, consumption of both goods and services rise, while the trade-induced increase in consumption of goods exceeds that of services. In addition, declining trade barriers also reduce the relative price of goods and increase income levels, both triggering a shift in expenditures away from goods and into services. As a result of this trade-induced structural change in expenditures, the contribution from higher goods consumption declines, implying lower estimated gains from trade compared to a world with fixed expenditure shares. The ongoing process of structural change causes declining goodsexpendituresharesandimpliesthatgainsfromtradebecomemoresuppressedovertime. Thoughstructuralchangehasbeenasignificantdragonglobaltradegrowthoverrecentdecades, it has not been a particularly strong drag since the global financial crisis. Instead, the recent slowdownintradecanbeattributedtoalackoffactorsthathavehistoricallycausedtradetoriserelative toexpenditure. Indeed,ourpaperdemonstrateshowunusualthe1990sand2000swere: Evenasthe share of services in expenditure rose, international trade flows expanded, as input-output linkages proliferated across country borders. For the same reasons, however, our results indicate that world tradeasafractionofGDPmayhavepeaked,andsimilarpatternsofstructuralchangeprojectedinto thefutureforeshadowdeclinesinthismeasureofopenness. 35

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A Data Appendix This section describes the data used to construct the empirical counterfactual in Section 2 and to estimate the model in Section 4. These data cover 1970–2015 for 27 countries/regions: Australia, Austria, Belgium-Luxembourg, Brazil, Canada, China, Cyprus, Denmark, Finland, France, Germany,Greece,India,Indonesia,Ireland,Italy,Japan,Korea,Mexico,Netherlands,Portugal,Spain, Sweden,Turkey,UnitedKingdom,andUnitedStates,plusa“RestofWorld”. Theempiricalcounterfactual requires time series of 1) total exports and imports of goods and services and 2) value added in goods and services. The model estimation requires these series as well as 3) bilateral goodsandservicestradedata;4)input-outputcoefficients;5)valueaddedtogrossoutputratios;6) sectoralpriceindices;and7)therealwage. OurstrategyistoworkwiththeWorldInput-OutputDatabase(WIOD)from1995-2011,which isdescribedinTimmer, Dietzenbacher, Los, StehreranddeVries(2015), thenbuildtherestofthe time sample out from those numbers using splicing techniques with other longer-running datasets. This ensures that the WIOD-based input-output coefficients generate sensible expenditure shares during WIOD years- otherwise, the input-output coefficients would be applied to trade data that maynotmatchtheunderlyingWIODdatausedtogeneratethosecoefficients. Totalexportsandimportsbycountry Foreachofthe27groupingsabove, wetaketotalgoods and services exports and imports from the WIOD from 1995-2011. Then, for all other years (i.e. 1970-1994and2012-2015),wesplicewithotherdata. Thesplicingproceduredividestheaverageof threeyearsoftheWIODdatabytheaverageofthreeyearsofalongerdatasettogenerateasplicing factor,thenapplyingthatsplicingfactortothelongerdatasetinnon-WIODyears. Theaveragesare calculatedfrom1995-1997forallyearsbefore1995, andfrom2009-2011forallyearsafter2011. Forgoodstrade,wesplicetheWIODtradedatawithworldtradefromtheIMFDirectionofTrade Statistics(IMF2016a)database. Forservices,weuseaggregateservicestradedatafromtheWorld Development Indicators (WDI) as the comparison. If WDI data on services is not available, we supplementingrowthrateswherenecessarywithOECDservicesdata. Value added For value added data, we rely on the UN Main Aggregates Database (UN (2017)). Wetakenominalgoodsvalueaddedinacountrytobethecombinationofexpenditurein“Agriculture,hunting,forestry,fishing”and“Mining,Manufacturing,Utilities”,whileservicesvalueadded isexpenditurein“Construction”,“Wholesale,retailtrade,restaurantsandhotels”,“Transport,storage,andcommunication”,and“OtherActivities”.23 23Results are qualitatively similar defining construction as a goods category, but given the lack of direct trade in construction,categorizingitasaservicewillmakegoodssectoralopennesslowerandservicessectoralopennesshigher. Both the model-based counterfactual and especially the reduced-form counterfactual would be smaller in magnitude relativetothedata. 39

Bilateral goods and services trade As with total goods trade, when not taken directly from the WIOD,goodstradebetweentwodifferentregionsinoursampleisgeneratedbysplicingimporterreported bilateral goods trade data in the IMF DOTS database with WIOD data, using the same three-yearcombinationsasabove. Bilateralservicesdataissparse,soinsteadofsplicing,wesimply apply average bilateral shares over three year periods to the total services trade data calculated as above. Again, for all years prior to 1995, we use average bilateral shares from 1995-1997, and for allyearsafter2011,weuseaveragebilateralsharesfrom2009-2011. Input-outputcoefficientsandvalueaddedtogrossoutputratios Toconstructγ ,thecountryikn specific share of intermediate inputs sourced from sector n, we use the numbers directly from WIOD. The value added to gross output ratio in sector k, λ is also a straightforward manipulaik tionofdataintheWIOD.Inbothcases,weuse1995coefficientsforyearspriorto1995,and2011 coefficientsforyearsafter2011. Sectoralprices Inordertoestimatethepreferenceparametersε ,ω andσ,weneedgross-output k k sectoral prices. First, we take nominal and real value added (indexed to 2005) data in goods and servicesfromtheUNMainAggregatesDatabase. Wegeneratesectoralpricesforeachsectorasthe ratioofnominaltorealvalueadded. WethenmultiplythesectoralvalueaddedindicesinPPPterms fromtheGGDCProductivityLevelDatabase“2005Benchmark”(InklaarandTimmer2014)byour value added price terms to make the country-level price indices comparable to each other in each year. Finally,we“grossup”thevalueaddedpricesusingtheequationforthevalueaddeddeflatorin AppendixC4ofSposi(2016). Notethatthesepricesareonlyusedinourestimatingequationforthe preferenceparameters;thepriceindicesinthecalibrationofthemodelareseparatemodel-specific objects. The iterative procedure for deriving elements of the model, including prices, relies on our estimatesofthepreferenceparameters. Labor We take total employment data in the Penn World Tables as our measure of L that goes i intothemodel. Sincethisdataonlygoesthrough2014, wecreateasplicingfactorwithWDItotal employmentdatain2015inordertoestimatethemodelthrough2015. 40

B Solution Algorithm Thisappendixdetailsthesolutionalgorithmforeachperiodofthemodeleconomy. Equationsthat werefertoarelistedintable2. Foreachtimeperiod: • Guessthevectorofwages,w,acrosscountries. i • Computethesectoralunitcostsν andthesectoralpricesP usingconditions(S2)and(S3) ik ik jointly. • Computethesectoralbilateraltradesharesπ usingcondition(S1). ijk • Computetheper-capitatransfersfromtheglobalportfolioRusingcondition(G1). • ComputetheaggregatepricelevelsP andaggregateconsumptionindexesC usingconditions i i (D3)and(D4)simultaneously. • ComputesectoralconsumptionC usingcondition(D1). ik • ComputesectorallabordemandL usingcondition(S4). ik • ComputesectoralintermediateinputdemandM usingcondition(S5). ikn • ComputesectoralgrossabsorptionQ usingcondition(S6). ik • ComputesectoralgrossproductionY usingcondition(S7). ik • Defineexcessdemandasnetexportsminusnetcontributionstotheglobalportfolio: PY −PQ −(ρwL −RL) Zw = i i i i i i i i . i w i Condition(G2)requiresthatZw =0,foralli,inequilibrium. Ifthisisdifferentfromzeroin i atleastsomecountry,thenupdatethewagevectorasfollows: (cid:18) Zw(cid:19) w(cid:48) =w 1+κ i , i i L i wherew(cid:48)istheupdatedguessofwagesandκ ischosentobesufficientlysmallsothatw(cid:48)>0. i i Use the updated wage vector and repeat every step to get a new value for excess demand. Continuethisprocedureuntiltheexcessdemandissufficientlyclosetozeroineverycountry simultaneously. NotethatWalras’Lawensuresthatthelabormarketclearsineachcountry. 41

C Country Results In this appendix, we break down structural change and the structural model-based counterfactual for each country in our sample and highlight their contribution to the aggregate counterfactual. Figure 18 shows the goods and services expenditure shares for each country and the rest of world aggregate. In all countries, the expenditure share of goods is falling, though for some countries, includingGreece,Mexico,andSweden,theshiftismoregradual. Figure19showsthebaselinemodelsolutionandthemodel-basedcounterfactualresultholding expenditure shares fixed for each country. The trade to expenditure ratio in the counterfactual is higherforeverycountry,thoughbystarklydifferentamounts. Thecounterfactualtendstobemore consistent in percent, rather than percentage point, terms across countries. For example, Belgium- Luxembourg starts out with a high degree of openness, and the counterfactual is about 50 percent higherthanthebaseline. Thesameisroughlytrueforothercountries, likeIndiaandJapan, witha farlowerdegreeofopenness. For some countries, however, the counterfactual level of openness is not much greater. This tends to relate directly to the degree to which the countries are experiencing structural change: Greece,Mexico,andSwedenallhavefairlymodestincreasesintheiropennessinthemodel-based counterfactual,whichechoestheirmodeststructuralchangefromfigure18. Table4showsthecontributiontotheaggregatefixedexpenditurecounterfactualdepictedinfigure8fortheyear2015,thelastyearofthesample. Thefirstcolumnprovidestheexpenditureshare of each country in the world aggregate, while the second is its trade share (exports plus imports in each country as a share of world trade). The third column represents the percentage point contribution of each country to the difference between the model-based counterfactual and the baseline, whichsumsto0.236orabout23percentagepoints. Thefinalcolumnshowstheequivalentpercent contribution. The table makes clear that the contribution to the aggregate counterfactual largely follows the country’s trade share, not its expenditure share. For example, with the United States being relatively closed, with an expenditure share about twice its trade share, the contribution of theU.S.totheaggregatecounterfactualisclosetothetradeshare. Bycontrast,Chinahasasimilar trade share and a smaller expenditure share and contributes the most of any single country to the aggregatecounterfactual. 42

Figure18: Sectoralexpendituresharesbycountry AUS AUT BLX BRA CAN 1 1 1 1 1 0.8 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.2 0 0 0 0 0 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 CHN CYP DEU DNK ESP 1 1 1 1 1 0.8 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.2 0 0 0 0 0 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 FIN FRA GBR GRC IDN 1 1 1 1 1 0.8 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.2 0 0 0 0 0 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 IND IRL ITA JPN KOR 1 1 1 1 1 0.8 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.2 0 0 0 0 0 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 MEX NLD PRT SWE TUR 1 1 1 1 1 0.8 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.2 0 0 0 0 0 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 USA ROW 1 1 0.8 0.8 0.6 0.6 Goods Services 0.4 0.4 0.2 0.2 0 0 19701980199020002010 1970 1980 1990 2000 2010 43

Figure19: Tradetoexpenditureratiobycountry AUS AUT BLX BRA CAN 3 3 3 3 3 2 2 2 2 2 1 1 1 1 1 0 0 0 0 0 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 CHN CYP DEU DNK ESP 3 3 3 3 3 2 2 2 2 2 1 1 1 1 1 0 0 0 0 0 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 FIN FRA GBR GRC IDN 3 3 3 3 3 2 2 2 2 2 1 1 1 1 1 0 0 0 0 0 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 IND IRL ITA JPN KOR 3 3 3 3 3 2 2 2 2 2 1 1 1 1 1 0 0 0 0 0 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 MEX NLD PRT SWE TUR 3 3 3 3 3 2 2 2 2 2 1 1 1 1 1 0 0 0 0 0 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 19701980199020002010 USA ROW 3 3 2 2 Baseline Fixed Expenditure 1 1 0 0 19701980199020002010 19701980199020002010 44

Table4: Contributionstofixedexpenditurecounterfactualin2015 Country ExpenditureShare TradeShare Contribution Pct. Contribution Australia 1.6% 1.7% 0.004 1.8% Austria 0.4% 1.2% 0.003 1.2% Belgium-Luxembourg 0.6% 2.3% 0.005 2.1% Brazil 2.2% 1.5% 0.005 2.0% Canada 2.1% 3.0% 0.006 2.4% China 15.2% 12.8% 0.032 13.8% Cyprus 0.0% 0.0% 0.000 0.0% Germany 3.5% 6.6% 0.018 7.6% Denmark 0.3% 0.9% 0.001 0.5% Spain 1.5% 2.3% 0.007 2.8% Finland 0.3% 0.5% 0.001 0.5% France 3.1% 3.9% 0.011 4.7% UnitedKingdom 3.6% 4.0% 0.009 4.0% Greece 0.3% 0.3% 0.000 0.0% Indonesia 1.2% 1.1% 0.003 1.1% India 2.7% 2.3% 0.005 2.1% Ireland 0.3% 1.0% -0.001 -0.3% Italy 2.2% 3.2% 0.009 3.7% Japan 6.1% 4.5% 0.013 5.4% Korea 1.6% 3.4% 0.010 4.1% Mexico 1.5% 2.3% 0.004 1.9% Netherlands 0.7% 1.9% 0.004 1.7% Portugal 0.3% 0.4% 0.001 0.6% Sweden 0.6% 1.2% 0.002 0.8% Turkey 1.0% 1.2% 0.003 1.4% UnitedStates 26.4% 13.5% 0.026 11.0% RestofWorld 20.9% 23.1% 0.054 22.9% Total 100.0% 100.0% 0.236 100.0% 45